
For the power flow, the linearized distribution flow (LDF) model proposed in [1]} is followed. Despite being an approximation for the full AC power flow model, LDF has been used extensively and shown to perform well in literature [2]}. Thus, ignoring line losses, the power balance at each node entails:
\(\sum _{e_{ij}\in \mathcal {E}} P_{ij} - \sum _{e_{jk}\in \mathcal {E}} P_{jk} = p_j \quad \forall {j\in \mathcal {V}}\\\sum _{e_{ij}\in \mathcal {E}} Q_{ij} - \sum _{e_{jk}\in \mathcal {E}} Q_{jk} = q_j \quad \forall {j\in \mathcal {V}}\) 
